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Chapter 2 Review Concepts and Vocabulary

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Q1. If a function is defined by the equation y = f(x), then x is called the _?_ variable and y is the _?_ variable.

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A1. independentdependent

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Q2. A set of points in the xy- plane is the graph of a function if and only if every _?_ line intersects the graph in at most one point.

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A2. vertical

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Q3. The set of all images of the elements in the domain of a function is called the _?_.

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A3. range

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Q4. True or False: Every relation is a function.

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A4. False

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Q5. True or False: The y-intercept of the graph of the function y = f(x), whose domain is all real numbers, is f(0).

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A5. True

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Q6. True or False: The independent variable is sometimes referred to as the argument of the function.

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A6. True

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Q7. For the graph of the linear function f(x) = mx + b, m is the _?_ and b is the _?_.

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A7. slopey-intercept

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Q8. True or False: The correlation coefficient is a measure of the strength of a linear relation between two variables and must lie between -1 and 1, inclusive.

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A8. True

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Q9. The average rate of change of a function equals the _?_ of the secant line.

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A9. slope

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Q10. A function f is _?_ on an open interval if for any choice of x 1 and x 2 in the interval, with x 1

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A10. increasing

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Q11. An _?_ function f is one for which f(-x) = f(x) for every x in the domain of f.

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A11. even

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Q12. An _?_ function f is one for which f(-x) = -f(x) for every x in the domain of f.

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A12. odd

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Q13. True or False: Even functions have graphs that are symmetric with respect to the origin.

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A13. false

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Q14. The graph of f(x) = mx + b is decreasing if m is _?_ than zero.

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A14. less

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Q15. When functions are defined by more than one equation, they are called _?_ functions.

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A15. piecewise

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Q16. True or False: The cube function is odd and is increasing on the interval (- ∞, ∞).

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A16. true

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Q17. True or False: The domain and range of the reciprocal function are the set of all real numbers.

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A17. false

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Q18. Given f(x), then the graph of y = f(x – 2) may be obtained by a(n) _?_ shift of the graph of f a distance of 2 units to the _?_.

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A18. horizontalright

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Q19. Given f(x), then the graph of y = f(-x) may be obtained by a reflection about the _?_-axis of the graph of the function y = f(x).

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A19. y

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Q20. Given f(x), then the graph of y = 3f(x) may be obtained by a vertical _?_ of the graph of f by a factor of _?_.

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A20. stretch3

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Q21. True or False: The graph of y = - f(x) is the reflection about the x-axis of the graph of y = f(x).

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A21. true

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Q22. True or False: To obtain the graph of y = f(x+2) – 3, shift the graph of y = f(x) horizontally to the right 2 units and vertically down 3 units.

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A22. false

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Q23. True or False: To obtain the graph of y = f(4x), horizontally compress the graph of y = f(x) by a factor of 4. That is, divide each x- coordinate on the graph of y = f(x) by 4.

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A23. true

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Q24. If the domain of f is all real numbers in the interval [0,7], and the domain of g is all real numbers in the interval [-2,5], then the domain of f + g is all real numbers in the interval _?_.

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A24. [0,5]

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Q25. The domain of f/g consists of all real numbers x for which g(x) _?_ 0 that are in the domains of both _?_ and _?_.

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A25. ≠fg

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Q26. If f(x) = x + 1 and g(x) = x³, then _?_ = (x + 1)³.

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A26. g(f(x))

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Q27. True or False: f(g(x)) = f(x)· g(x)

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A27. false

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Q28. True or False: The domain of (f· g)(x) consists of the numbers x that are in the domains of both f and g.

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A28. true

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Q29. True or False: The domain of the composite function (f ◦ g)(x) is the same as the domain of g(x).

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A29. false

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Q30. What is the best way to study for a Math test?

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A30. Work problems!

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